Spherical Convolution – A Theoretical Walk-Through

Convolution is an extremely effective technique that can capture useful features from data distributions. Specifically, convolution based deep neural networks have performed exceedingly well on 2D representation learning tasks, e.g. image analysis. Given this success, it is natural to investigate how to use this concept to capture features in different settings. However, most state-of-the-art deep neural networks work only on Euclidean geometries and extending this concept to other manifolds such as spheres and balls is an open research problem. Representing data in spheres/balls can be quite natural and effective in cases such as analyzing 3D data. However, achieving this task is not straightforward. The main difficulty of adapting convolution to such manifolds is that in contrast to planar data, the spaces between adjacent points are not uniform.Read the article on medium.com >